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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today, we're going to learn how to solve linear equations. Does anyone know what a linear equation looks like?
Isn't it something like 2x + 5 = 11?
Exactly! That's a great example. To solve it, we need to isolate our variable, x. What do you think we should do first?
We should subtract 5 from both sides?
Correct! So what do we get after that?
2x = 6!
Well done! Now, what’s the next step?
We divide by 2 to find x!
Yes, and what do we get?
x = 3!
Fantastic! Remember, the steps are: isolate the variable, perform inverse operations, and check your work.
Now let's apply that knowledge. Solve the equation 4x - 8 = 0. Who wants to start?
First, we add 8 to both sides!
Good start! What does that leave us with?
4x = 8!
Excellent! Now, what do we do next?
Divide both sides by 4 to find x.
That's right! So, what's x?
x = 2!
Awesome! Remember that solving is about isolating the variable. Keep practicing!
Let’s talk about checking our solutions. Why do you think that’s important?
To make sure our answer is correct?
That's right! I'll show you how to verify the solution to our previous example, 4x - 8 = 0. If x = 2, what would you do?
Substitute 2 back into the equation.
Yes, and what do we get?
4(2) - 8 = 0! Which means it's correct!
Exactly! Always substitute back to verify your results.
Isolate the x, don’t let it stress, follow steps and you’ll impress!
In the kingdom of Algebra, the wise king would always find a way to free x from the constraints of numbers, teaching all the villagers to apply inverse operations to uncover the truth of x’s identity.
I.S.O.L.A.T.E.: Isolate Step One: Operations Leading to Answering the Equation.
To remember the process, think 'S.I.G.N': Substitute, Isolate, Get the answer, Verify!
Term
x in 2x + 4 = 12
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Term
Isolate x
Click to flip
An equation that forms a straight line when graphed, typically expressed as 𝑎𝑥 + 𝑏 = 𝑐.
To manipulate an equation so that one variable is alone on one side of the equation.
Operations that reverse the effect of another operation, such as addition/subtraction or multiplication/division.
Replacing a variable with a number to check if the equation holds true.
This section focuses on solving linear equations to find the values of variables that make the equation true.
In this section, students will learn how to solve linear equations step-by-step, understand the significance of isolating the variable, and practice through multiple examples. The concept of linear equations is vital in algebra, facilitating understanding across various applications.
Solving linear equations is a fundamental skill in algebra. A linear equation is an expression of the form 𝑎𝑥 + 𝑏 = 𝑐, where 𝑎, 𝑏, and 𝑐 are constants, and 𝑥 is the variable we aim to solve for. The primary goal in solving these equations is to isolate 𝑥 on one side of the equation to determine its value.
Solve the equation 2𝑥 + 5 = 11
This process not only aids in solving basic equations but also lays the groundwork for more complex problem-solving in higher algebra and beyond.